knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) library("riskyr") # load the "riskyr" package
The greatest value of a picture is when it forces us to notice what we never expected to see.
(John W. Tukey)^[Tukey, J.W. (1977), Exploratory data analysis. Reading, MA: Addison-Wesley. (p. vi).]
The riskyr
data structures essentially describe networks of dependencies.
This is best illustrated by the network diagram (see examples of plot_fnet
in the
user guide and data formats).
However, sometimes it is instructive to view all possible values of some parameter
as a function of others. A functional perspective illustrates how the value of
some parameter (or its values) changes as a function of other parameters
(and their values).
The basic format of a function is $y = f(x)$, which illustrates how values of $y$
depend on values of $x$ given some function $f$. riskyr
provides 2 functions for
viewing parameters as a function of other parameters (and their values).
The function plot_curve
draws the curves (or lines) of selected parameters as a function of the prevalence (with prev
ranging from 0 to 1)
for a given decision process or diagnostic test (i.e., given values of sens
and spec
):
$$y \ = \ f(\texttt{prev} \textrm{, from 0 to 1}) \textrm{ with } y \in {\texttt{PPV}, \texttt{NPV}, \texttt{ppod}, \texttt{acc}} \ \ \ \ \ \ (1)$$
As an example, reconsider our original scenario (on mammography screening, see user guide). Earlier, we computed a positive predictive value (PPV) of 7.8%. But rather than just computing a single value, we could ask: How do values of PPV develop as a function of prevalence? The plot_curve
function illustrates this relationship:
plot_curve(prev = .01, sens = .80, spec = (1 - .096), what = c("prev", "PPV", "NPV"), title_lbl = "Mammography screening", cex.lbl = .8)
The curves illustrate that values of PPV
and NPV
crucially depend on the value of prevalence prev
in the current population. In fact, they actually vary across their entire range (i.e., from 0 to 1), rendering any communication of their value utterly meaningless without specifying the current population's prevalence value prev
.
The dependency of PPV
and NPV
on prev
can be illustrated by assuming a higher prevalence rate. For instance, if we knew that some woman was genetically tested and known to exhibit the notorious BRCA1 mutation, the prevalence value of her corresponding population (given a positive mammography result in a routine screening) is increased to about 60% (graph not shown here to save space, but try running the following code for yourself):
high.prev <- .60 # assume increased prevalence due to BRCA1 mutation plot_curve(prev = high.prev, sens = .80, spec = (1 - .096), what = c("prev", "PPV", "NPV"), title_lbl = "Mammography screening (BRCA1 mutation)", cex.lbl = .80)
This shows that --- given an increased prevalence value prev
of 60% --- the positive predictive value PPV
of a positive test result increases from 7.8% (in the standard population) to around 93% (given the BRCA1 mutation).
In addition, the actual values of population and test parameters are often unclear. The plot_curve
function reflects this by providing an uncertainty parameter uc
that is expressed as a percentage of the specified value. For instance, the following assumes that our parameter values may deviate up to 5% from the specified values and marks the corresponding ranges of uncertainty as shaded areas around the curves that assume exact parameter values.
Both the notions of expressing probabilities as a function of prevalence and of uncertainty ranges for imprecise parameter estimates can be extended to other probabilities. The following curves show the full set of curves currently drawn by plot_curve
. In addition to the predictive values PPV
and NPV
, we see that the proportion of positive decisions ppod
and the overall accuracy acc
also vary as a function of prevalence prev
:
high.prev <- .60 # assume increased prevalence due to BRCA1 mutation plot_curve(prev = high.prev, sens = .80, spec = (1 - .096), what = c("prev", "PPV", "NPV", "ppod", "acc"), title_lbl = "Mammography screening (BRCA1 mutation)", uc = .05, cex.lbl = .80)
The function plot_plane
draws a plane for a selected parameter as a function of sensitivity and specificity
(with sens
and spec
both ranging from 0 to 1) for a given prevalence prev
:
$$y \ = \ f(\texttt{sens} \times\ \texttt{spec} \textrm{, both from 0 to 1, for given value of } \texttt{prev}) \textrm{ with } y \in {\texttt{PPV}, \texttt{NPV}, \texttt{ppod}, \texttt{acc}} \ \ \ \ \ \ \ (2)$$
Some examples (not shown here, but please try evaluating the following function calls):
plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "PPV", title_lbl = "A. Mammography (BRCA1)", cex.lbl = .8)
Related plots (showing different probabilities) include:
plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "NPV", title_lbl = "B. Mammography (BRCA1)", cex.lbl = .8) plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "ppod", what_col = "firebrick", title_lbl = "C. Mammography (BRCA1)", phi = 45, cex.lbl = .8) plot_plane(prev = high.prev, sens = .80, spec = (1 - .096), what = "acc", what_col = "forestgreen", title_lbl = "D. Mammography (BRCA1)", cex.lbl = .8)
Overall, viewing conditional probabilities (like PPV
/NPV
, but also ppod
and acc
) as a function of other probabilities (e.g., prev
, sens
, spec
or fart
) often provides unexpected relationships and new insights.
The following resources and versions are currently available:
Type: | Version: | URL: |
:------------------------|:-------------------|:-------------------------------|
A. riskyr
(R package): | Release version | https://CRAN.R-project.org/package=riskyr |
\ | Development version | https://github.com/hneth/riskyr |
B. riskyrApp
(R Shiny code): | Online version | http://riskyr.org |
\ | Development version | https://github.com/hneth/riskyrApp |
C. Online documentation: | Release version | https://hneth.github.io/riskyr |
\ | Development version | https://hneth.github.io/riskyr/dev |
We appreciate your feedback, comments, or questions.
Please report any riskyr
-related issues at https://github.com/hneth/riskyr/issues.
Email us at contact.riskyr@gmail.com if you want to modify or share this software.
| Nr. | Vignette | Content |
| ---: |:---------|:-----------|
| A. | User guide | Motivation and general instructions |
| B. | Data formats | Data formats: Frequencies and probabilities |
| C. | Confusion matrix | Confusion matrix and accuracy metrics |
| D. | Functional perspectives | Adopting functional perspectives |
| E. | Quick start primer | Quick start primer |
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